Emanuele Dotto Associate Professor Office: C1.18 Email: Emanuele dot Dotto at warwick dot ac dot uk

 

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Teaching Responsibilities 2022/23:

Term 2: MA4M6 category theory

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Research Interests

Algebraic topology, in particular algebraic and Hermitian K-theory, topological Hochschild and cyclic homology, equivariant homotopy theory, calculus of functors.

Here is my CVLink opens in a new window.

I am an editor of the Journal and Bulletin of the London Mathematical SocietyLink opens in a new window.

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Seminars

We have an ongoing Warwick algebraic topology seminarLink opens in a new window during term time.

Past reading seminars:

2022/2023

• The working seminarLink opens in a new window

2021/2022

• Reading seminar on The Adams spectral sequence and Franke's algebraicity conjectureLink opens in a new window
• Reading seminar on cyclotomic spectra and Cartier modulesLink opens in a new window

2020/2021

• Working seminar on Poincaré categories and forms
• Working seminar in algebraic topologyLink opens in a new window

2019/2020

• Reading seminar on topological cyclic homology

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Articles

• An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2Link opens in a new window,

  preprint 2024.

• Witt vectors with coefficients and TRLink opens in a new window, with Achim Krause, Thomas Nikolaus and Irakli Patchkoria,

  preprint 2023.

• On the geometric fixed-points of real topological cyclic homologyLink opens in a new window, with Kristian Moi and Irakli Patchkoria,

  Journal of the London Mathematical Society, Volume 109, Issue 2, (2024), https://doi.org/10.1112/jlms.12862

• Hermitian K-theory for stable infinity-categories I: FoundationsLink opens in a new window, with Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle,

  Selecta Mathematica New Ser. 29, 10 (2023). https://doi.org/10.1007/s00029-022-00758-2.

• Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivityLink opens in a new window, with Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle,

  preprint 2020.

• Hermitian K-theory for stable infinity-categories III: Grothendieck-Witt groups of ringsLink opens in a new window, with Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle,

  preprint 2020.

• Witt vectors with coefficients and characteristic polynomials over non-commutative ringsLink opens in a new window, with Achim Krause, Thomas Nikolaus and Irakli Patchkoria,

  Compositio Mathematica , Volume 158 , Issue 2 , February 2022 , pp. 366 - 408, DOI: https://doi.org/10.1112/S0010437X22007254 .

• Witt vectors, polynomial maps, and real topological Hochschild homologyLink opens in a new window, with Kristian Moi and Irakli Patchkoria,

  Annales scientifiques de l'école normale supérieure, Tome 55, Fasc. 2, pp 473-535, 2022, DOI: 10.24033/asens.2500.

• Hermitian K-theory of Mackey functors, real traces, and assemblyLink opens in a new window, with Crichton Ogle,

  Annals of K-theory 4-2 (2019), 243--316. DOI 10.2140/akt.2019.4.243.

• Real topological Hochschild homologyLink opens in a new window, with Kristian Moi, Irakli Patchkoria and Sune Precht-Reeh,

  J. Eur. Math. Soc. (JEMS) 23 (2021), no. 1, 63–152.

• Comparing cyclotomic structures on different models for topological Hochschild homologyLink opens in a new window, with Cary Malkiewich, Irakli Patchkoria, Steffen Sagave, Calvin Woo,

  Journal of Topology, 12 (2019), no. 4, 1146-1173.

• Higher equivariant excisionLink opens in a new window,

  Advances in Mathematics, 309 (2017), 1-96.

• A Dundas-Goodwillie-McCarthy theorem for split square-zero extensions of exact categoriesLink opens in a new window,

  An alpine bouquet of algebraic topology, Contemp. Math. 708, Amer. Math. Soc., 2018.

• Parametrized higher category theory and higher algebra: Exposé I -- Elements of parametrized higher category theoryLink opens in a new window, with Clark Barwick, Saul Glasman, Denis Nardin, Jay Shah,

  preprint 2016.

• Parametrized higher category theory and higher algebra: A general introductionLink opens in a new window, with Clark Barwick, Saul Glasman, Denis Nardin, Jay Shah,

  preprint 2016.

• Equivariant diagrams of spacesLink opens in a new window,

  Algebr. Geom. Topol. 16 (2016), no. 2, 1157-1202.

• Homotopy theory of G-diagrams and equivariant excisionLink opens in a new window, with Kristian Moi,

  Algebr. Geom. Topol. 16 (2016), no. 1, 325-395.

• Equivariant calculus of functors and Z/2-analyticity of real K-theoryLink opens in a new window,

  Journal of the Institute of Mathematics of Jussieu, Volume 15, Issue 4, October 2016, pp. 829-883.

• A relative h-principle via cobordism-like categoriesLink opens in a new window,

  An Alpine Expedition through Algebraic Topology , Contemp. Math. 617, Amer. Math. Soc., 2014.

• Stable real K-theory and real topological Hochschild homologyLink opens in a new window,

  Phd thesis, 2012.

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Recent research grants

EPSRC New Investigator Award, 2022-2025.

Funding from German Research Foundation Schwerpunkt-programm 1786, 2018-2019.